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Related Concept Videos

Hypothesis Test for Test of Independence01:16

Hypothesis Test for Test of Independence

The test of independence is a chi-square-based test used to determine whether two variables or factors are independent or dependent. This hypothesis test is used to examine the independence of the variables. One can construct two qualitative survey questions or experiments based on the variables in a contingency table. The goal is to see if the two variables are unrelated (independent) or related (dependent). The null and alternative hypotheses for this test are:
H0: The two variables (factors)...
Introduction to Test of Independence01:21

Introduction to Test of Independence

In statistics, the term independence means that one can directly obtain the probability of any event involving both variables by multiplying their individual probabilities. Tests of independence are chi-square tests involving the use of a contingency table of observed (data) values.
The test statistic for a test of independence is similar to that of a goodness-of-fit test:
Test for Homogeneity01:23

Test for Homogeneity

The goodness–of–fit test can be used to decide whether a population fits a given distribution, but it will not suffice to decide whether two populations follow the same unknown distribution. A different test, called the test for homogeneity, can be used to conclude whether two populations have the same distribution. To calculate the test statistic for a test for homogeneity, follow the same procedure as with the test of independence. The hypotheses for the test for homogeneity can be stated as...
Chi-square Distribution01:10

Chi-square Distribution

How does one determine if bingo numbers are evenly distributed or if some numbers occurred with a greater frequency? Or if the types of movies people preferred were different across different age groups or if a coffee machine dispensed approximately the same amount of coffee each time. These questions can be addressed by conducting a hypothesis test. One distribution that can be used to find answers to such questions is known as the chi-square distribution. The chi-square distribution has...
Chi-square Analysis02:46

Chi-square Analysis

The chi-square test is a statistical hypothesis test. It is used to check whether there is a significant difference between an expected value and an observed value. In the context of genetics, it enables us to either accept or reject a hypothesis, based on how much the observed values deviate from the expected values.
The chi-square test was developed by Pearson in 1990.
The first step of performing a Chi-square analysis is to establish a null hypothesis, which assumes that there is no real...
Goodness-of-Fit Test01:16

Goodness-of-Fit Test

The goodness-of-fit test is a type of hypothesis test which determines whether the data "fits" a particular distribution. For example, one may suspect that some anonymous data may fit a binomial distribution. A chi-square test (meaning the distribution for the hypothesis test is chi-square) can be used to determine if there is a fit. The null and alternative hypotheses may be written in sentences or stated as equations or inequalities. The test statistic for a goodness-of-fit test is given as...

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The chi-square test of independence.

Mary L McHugh1

  • 1Department of Nursing, School of Health and Human Services, National University, Aero Court, San Diego, California, USA. mchugh8688@gmail.com

Biochemia Medica
|July 31, 2013
PubMed
Summary

The Chi-square statistic is a versatile, non-parametric tool for analyzing group differences with nominal data. It offers detailed insights and flexibility, especially when parametric assumptions are unmet, though sample size and interpretation with many categories are limitations.

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Area of Science:

  • Statistics
  • Biostatistics
  • Social Sciences Statistics

Background:

  • The Chi-square statistic is a non-parametric tool for analyzing group differences with nominal dependent variables.
  • It is robust to data distribution, not requiring equal variances or homoscedasticity.

Purpose of the Study:

  • To detail the Chi-square statistic's utility in analyzing group differences.
  • To highlight its advantages, including robustness, ease of computation, and detailed information derivation.
  • To discuss its application in studies where parametric assumptions cannot be met.

Main Methods:

  • The Chi-square statistic is employed for analyzing nominal level dependent variables across two or more independent groups.
  • It allows for the evaluation of dichotomous and multiple-group independent variables.
  • Significance is assessed using Chi-square, followed by a strength statistic like Cramer's V.

Main Results:

  • The Chi-square statistic provides detailed information on group performance, offering richer insights than many other statistics.
  • It is flexible for both two-group and multiple-group studies.
  • Cramer's V is commonly used to measure the strength of association for significant Chi-square results.

Conclusions:

  • The Chi-square statistic is a valuable, robust, and flexible tool for analyzing nominal data, particularly when parametric assumptions are violated.
  • Researchers can derive detailed insights from Chi-square analyses.
  • Limitations include sample size requirements and potential interpretation difficulties with numerous categories, alongside Cramer's V's tendency for low correlation measures.